In terms of whether or not you can hit 700+, I would look at your practice scores for the answer. If you have hit 700+ on at least 20-30% of your practice tests (including
MGMAT, PR, and GMATPrep, but not Kaplan), then I would say you have a shot. But if you have not done this, I would say getting a 570, 660 and then pulling off a 700+ in just 3 weeks is a huge stretch and I would encourage you to take a bit more time (5-6 weeks) to ensure you really get the core concepts and timing down perfectly.
Marcus